Statistical Science

Oracle, Multiple Robust and Multipurpose Calibration in a Missing Response Problem

Kwun Chuen Gary Chan and Sheung Chi Phillip Yam

Full-text: Open access

Abstract

In the presence of a missing response, reweighting the complete case subsample by the inverse of nonmissing probability is both intuitive and easy to implement. When the population totals of some auxiliary variables are known and when the inclusion probabilities are known by design, survey statisticians have developed calibration methods for improving efficiencies of the inverse probability weighting estimators and the methods can be applied to missing data analysis. Model-based calibration has been proposed in the survey sampling literature, where multidimensional auxiliary variables are first summarized into a predictor function from a working regression model. Usually, one working model is being proposed for each parameter of interest and results in different sets of calibration weights for estimating different parameters. This paper considers calibration using multiple working regression models for estimating a single or multiple parameters. Contrary to a common belief that overfitting hurts efficiency, we present three rather unexpected results. First, when the missing probability is correctly specified and multiple working regression models for the conditional mean are posited, calibration enjoys an oracle property: the same semiparametric efficiency bound is attained as if the true outcome model is known in advance. Second, when the missing data mechanism is misspecified, calibration can still be a consistent estimator when any one of the outcome regression models is correctly specified. Third, a common set of calibration weights can be used to improve efficiency in estimating multiple parameters of interest and can simultaneously attain semiparametric efficiency bounds for all parameters of interest. We provide connections of a wide class of calibration estimators, constructed based on generalized empirical likelihood, to many existing estimators in biostatistics, econometrics and survey sampling and perform simulation studies to show that the finite sample properties of calibration estimators conform well with the theoretical results being studied.

Article information

Source
Statist. Sci., Volume 29, Number 3 (2014), 380-396.

Dates
First available in Project Euclid: 23 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.ss/1411437519

Digital Object Identifier
doi:10.1214/13-STS461

Mathematical Reviews number (MathSciNet)
MR3264551

Zentralblatt MATH identifier
1331.62070

Keywords
Generalized empirical likelihood model misspecification missing data robustness

Citation

Chan, Kwun Chuen Gary; Yam, Sheung Chi Phillip. Oracle, Multiple Robust and Multipurpose Calibration in a Missing Response Problem. Statist. Sci. 29 (2014), no. 3, 380--396. doi:10.1214/13-STS461. https://projecteuclid.org/euclid.ss/1411437519


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Supplemental materials

  • Supplementary material: Proof of the Main Results. Online supplementary material is provided that includes a list of regularity conditions, the proofs of Lemma 1, Theorem 2 and Corollary 3, together with two technical lemmas that were needed to prove Lemma 1.